JPH0833425B2 - Digital fault locator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial application] The present invention relates to a digital fault locator for a power system.

[Conventional technology]

FIG. 6 is a diagram showing an electric power system to which the fault point locating device is applied. (1) is a generator, (2) is a bus bar, (3) is a transmission line, (4) is a fault point, and (5) is Current transformer, (6) transformer, (10) digital fault locator, (11) circuit for converting output of current transformer (5) to appropriate value, (12) transformer ( A circuit for converting the output of 6) to an appropriate value, (21) and (22) are filter circuits for removing the frequency band restricted from the sampling theorem, and (31) is a sampling of the input at regular intervals and sequential AD conversion. The circuit, (100), indicates an arithmetic circuit.

As a digital fault point locator, from the resistance R, inductance L and fault current i of the transmission line up to the fault point,
The bus voltage v is Since the relational expression of is established, we obtain two integral values (2) and (3) A method of obtaining R and L by solving simultaneous equations from these two equations is known.

By the way, in the calculation processing in the digital type, it is necessary to approximately obtain the integral by using discrete values sampled at constant time intervals, and thus this approximate expression has a frequency characteristic and is an error factor. As a method for improving this frequency characteristic, Japanese Patent Application No. 60-179640 "Digital Distance Relay" has been proposed.

[Problems to be solved by the invention]

In this method, the continuous sampling time is set to t _n , t _{n + 1} , and t _{n + 2} at regular intervals, and the current value sampled at each time is i _(n) , i _{(n + 1)} , i _{(n + 2)} , the integrated value of current is Since it is approximated by, there is a problem that the error becomes large in the higher frequency range.

The present invention has been made to solve the above problems, and it is an object of the present invention to obtain a digital fault locator which can improve frequency characteristics even in a higher frequency range. .

[Means for solving problems]

The present invention is obtained by integrating the relational expression occurring in the transmission system shown in the equation (1) from time t _n-1 to t _{n + 1} and from t _n to t _{n + 2} . By solving simultaneous equations from both equations
R and L are obtained, but at this time, the sampling frequency of an odd number of points is used, and the error occurring at the higher order frequency is multiplied by the correction coefficient and integrated approximation is performed to improve the higher order frequency characteristic. The present invention provides a fault location device.

[Action]

According to the integral approximation formula according to the present invention, the integral approximation error can be made zero for n + 1 frequencies by determining K ₁ , K ₂ ... K _{n + 1} by the method described later. The frequency characteristic of the L calculation error is improved.

Example of Invention

Embodiments of the present invention will be described below with reference to the drawings. Sixth
Referring to the figure, the arithmetic circuit (100) is composed of, for example, a microcomputer, and by calculating the following equation (4), it is possible to eliminate the error in the higher harmonics which is the object of the present invention.

However i _{(n + 1)} −i _(n) = B i _{(n + 1)} −i _(n-1) = D △ = EB-FD is shown.

FIG. 1 shows the arithmetic circuit (10
(111) to (11) in the block diagram for explaining the function of (0).
4) is a circuit for deriving the approximate integral, and (111) is the above-mentioned A, (11
2) is an arithmetic circuit that derives C, (113) is E, and (114) is F. (115) is a subtraction circuit for calculating B and (116) is for calculating D. (121) to (123) are arithmetic circuits, and (121)
AB-CD, (122) CE-AF, and (123) Δ. The division circuit (131) derives the resistance component R up to the failure point, and the division circuit (132) derives the inductance component L up to the failure point.

Since a digital fault point locating device can be obtained by obtaining the integrated value of the current voltage as described later, here, first, a method of obtaining these integrated values by using a digital amount will be described. FIG. 2 is a sine wave having an arbitrary single frequency and a waveform represented by the general formula i = sin (ωt + β). Here, β represents a phase angle with respect to a voltage vector (not shown).
i _(n-1) , i _(n) , i _{(n + 1)} is the current i at time t _n-1 , t _n , t _{n + 1}
The values derived by sampling with the respective instantaneous values are shown. Now, _assuming that the sampling times t _n-1 , t _n , and t _{n + 1} are equally spaced and the angle components are θ angles, from t _n-1
If the divided value of the current i up to t _{n + 1} can be obtained simply and approximately, it can be obtained as follows. That is, b ₁ −i _(n-1) −i _{(n + 1)} −
It can be approximated by the area of a quadrangle surrounded by a ₁ .

However, since various harmonics are generated when a system failure occurs, it is necessary that the integrated values obtained at this time be similar, but as shown in FIG. 8, 2 of the frequency components of FIG.
In this case, b ₁ −i _(n-1) −i _{(n + 1)} −
The area of the quadrilateral surrounded by a ₁ is a triangle in this case, but as you can see from the figure, the error is obviously larger than the true value. From this, it can be imagined that the sampling interval can be reduced.

That is, using an intermediate sample value, b ₁ −i _(n-1) −i _(n) −
a ₀ enclosed by a quadrilateral area and _{a 0 -i (n) -i (} n + 1) error amount from a method of the area of the quadrilateral surrounded by -a ₁ considered earlier by an addition Can be improved.

However, even in this case, when considering a higher-order high frequency, an error still exists, so that it is possible to further reduce the sampling interval, but there is a limit to this.

From such a viewpoint, in the present invention, a method of suppressing the error to a high frequency region of a high order by using a large number of sample values of odd points regardless of the sampling interval is considered. I'll explain.

In FIG. 2, when the integral value from time t _n-1 to t _{n + 1} is obtained as the sampling interval θ, the true value I is as follows.

Next, when the approximate integral value is S, the following equation is obtained.

Here, i _(n-1) = sin {ωt + β + (n-1) θ} i _(n) = sin (ωt + β + nθ) i _{(n + 1)} = sin {ωt + β + (n + 1) θ} Substituting into The (7) an approximate integral value corrected by multiplying the coefficient C in the equation (7) in order to approximate value obtained is the (5) being equal to the true value obtained by the formula in expression when placed as S _C S _C = Cθsin (ωt + β + nθ) (1 + cosθ)
(8)

Therefore, the coefficient to multiply the approximate value from equations (5) and (8) to be the true value is It turns out that

However, even with the approximate integral equation corrected in this way,
Considering the case where a higher harmonic of m times the frequency that has been considered so far is applied, the corrected approximate integral is expressed by C in Equation (6).
Multiply by Since the instantaneous value of i is i _(n-1) = sin {mωt + β + (n-1) mθi _(n) = sin (mωt + β + nmθi _{(n + 1)} = sin {mωt + β + (n + 1) mθ}, If you deploy the same as above Substituting equation (9) into the correction coefficient C Becomes

On the other hand, the true value of the integrated value is expanded in the same way as equation (5). Therefore, the error is calculated from Eqs. (11) and (12) Therefore, even if the corrected C is applied, an error occurs in the mth harmonic.

In the present invention, to correct these errors, the sampling interval is left unchanged and the sampling value of an odd number of points (provided that the number of points × θ <2π is satisfied) is used as shown in FIG. The equation is a polynomial, and each term is multiplied by a correction coefficient so that the error is zero at a specific frequency.

That is, in FIG. 4, add the areas of the quadrangle b ₁ −i _(n-1) −i _(n) −a ₀ and the quadrangle a ₀ −i _(n) −i _{(n + 1)} −a _1. Then, it becomes one term, and it is multiplied by the correction coefficient K ₁ so that the error becomes zero at the frequency of the fundamental wave. Is obtained in the same manner as the equation (6).

Next, in the area of the quadrangle b ₁ −i _(n-1) −i _{(n + 1)} −a ₁ , for example, 2
The correction coefficient K ₂ is multiplied so that the error becomes zero at the double frequency, and S ₁ = K ₂ θ {i _(n-1) + i _{(n + 1)} } is obtained.

Further, the area of the quadrangle b ₂ −i _(n-2) −i _{(n + 2)} −a ₂ is multiplied by a correction coefficient K ₃ so that the error is zero at a specific frequency, and S ₂ = 2K ₃ θ { i _(n-2) + i _{(n + 2)} } is obtained. Similarly, S _n-1 = K _{n (n-1)} θ {i ₍₁₎ + i _(2n-1) } S _n = K _{n + 1} nθ {i ₍₀₎ + i _(2n) } is obtained. And the sum of them Is an approximate integral formula.

Next, a method of calculating the correction coefficient in this equation will be described.

Now, assuming that the current waveform is a harmonic of the mth order and the instantaneous value of i at time t ₀ is i ₍₀₎ = sin (mωt + β) Therefore, substituting these values into equation (14) Get.

On the other hand, the true integral value from t _{n -1} to t _{n + 1} is Becomes

Therefore, if a correction coefficient is determined to make the approximate integrated value S _T equal to the true value, it can be obtained by using equations (15) and (16) as identities. , It seems that it becomes a value that is far from the true value depending on the number of repeated additions, but since it is corrected by multiplying the weighting coefficient for each area obtained from each term expression that repeats addition, it should be closer to the true value. Will be possible.) That is, if the similar terms in Eqs. (15) and (16) are deleted and shown by the identities Becomes

From this equation, a correction coefficient can be obtained by solving the simultaneous equations by creating an equation so that the error becomes zero at a specific frequency. For example, if the error is zero between the fundamental wave and the doubled frequency by using the sampling values of 3 points, the sampling points are 3 points of b ₁ , a ₀ , and a ₁ ; Is assigned n = 1.

Therefore, when formula (17) is created for the case of the fundamental wave, m = 1
By substituting θK ₁ (1 + cosθ) + 2θK ₂ cosθ = 2sinθ Next, when formula (17) is created for the case of double frequency, m = 2
By substituting θK ₁ {1 + cos (2θ)} + 2θK ₂ cos (2θ) = sin (2θ) The values of the correction coefficients K ₁ and K ₂ can be obtained by solving the determinant of.
The characteristic of Fig. 5 (200) is to calculate K ₁ and K ₂ with 3-point sampling at a sampling interval θ of 30 ° and substitute it into the approximate integral formula (14) to calculate the error from the true value on the vertical axis. To the fundamental frequency
The ratio / ₀ of the harmonic orders for ₀ which was drawn on the horizontal axis, is well known already been proposed for this three sampling.

According to the present invention, the error can be eliminated up to the harmonic range by increasing the number of used samplings with an odd number of points such as 5 points and 7 points.

For example, when there are 7 points, the sampling points are b ₃ , b ₂ , b ₁ , a
_{Since 0} , ... A ₃ , n = 3 is substituted for n in the equation (17). Here, if the error is zero in the fundamental wave, double frequency, triple frequency, and quadruple frequency components, the correction coefficients K ₁ ... K ₄ can be obtained by solving simultaneous equations from the following four equations. .

That is, when the fundamental wave, m = 1 is substituted and θK ₁ (1 + cos θ) + 2θK ₂ cos θ + 4 θK ₃ cos (2θ) +6 θK ₄ cos (3θ) = 2 sin (θ) At the time of double frequency, m = 2 is substituted and θK ₁ {1 + cos (2θ)} + 2θK ₂ cos (2θ) + 4θK ₃ cos (4θ) + 6θK ₄ cos (6θ) = sin (2θ) At triple frequency, substitute m = 3 Substituting m = 4 at quadruple frequency And from these expressions The correction coefficient K ₁ ... K ₄ can be obtained by solving the determinant of. The characteristic of FIG. 5 (300) shows the frequency characteristic when the correction coefficient is calculated by using this 7-point sampling with the sampling interval θ of 30 ° and the approximate integration of the equation (14) is performed.

Thus, by approximating the approximate integral by the equation (14) and determining the correction coefficient in the equation by the above-mentioned method, it is possible to eliminate the error up to higher harmonics and improve the frequency characteristic.

The approximate integral value thus obtained is used for the next integral term obtained from the simultaneous equations (2) and (3) described at the beginning of the description, Since the resistance component R and the inductance component L up to the fault point that has occurred in the power system can be obtained by calculating the above, the digital fault point locating device can be provided.

In the above, the method of integrating the current is described, but the fact that the integration of the voltage can be obtained in the same manner, and the hardware configuration of the embodiment of the present invention is the same as that of a normal digital relay and is already known. Details are omitted.

In the above explanation, voltage and current are not mentioned sometimes, but in a normal three-phase power system, the line voltage and line current in the case of a short-circuit fault locator, and the phase voltage in a ground fault locator. Needless to say, the phase current that compensates the zero-phase current is used.

In the fault point locator, the resistance component up to the fault point at high speed
In consideration of the fact that R and the inductance component L do not have to be calculated, the voltage and current at the time of a power system failure may be stored and later calculated using the stored values. For this reason, it is not a problem to use a large number of sampling values because it is more important to improve the accuracy.

Further, it goes without saying that the present invention can be applied to the distance relay by using many sampling values within the allowable range of the calculation time.

Further, it goes without saying that it can be used to obtain a scalar quantity of voltage and current.

〔The invention's effect〕

As described above, according to the present invention, since the correction coefficient is provided for the error in the high-order high frequency range, there is an effect that the frequency characteristic can be improved up to the high-order high frequency range.

[Brief description of drawings]

FIG. 1 is a block diagram for explaining the calculation function of the present invention, FIGS. 2 and 3 are diagrams for explaining the outline of the approximate integration, and FIG. 2 shows the waveform of the fundamental wave component. The figure shows the case of the waveform of the double frequency component. FIG. 4 is a diagram for explaining the principle of approximate integration according to the present invention, and FIG. 5 is a diagram showing frequency characteristics of integral approximation. (200) in the figure is a conventionally proposed characteristic,
(300) indicates the frequency characteristic improved by the present invention.
FIG. 6 is a diagram showing a power system to which the fault location device is applied. The same reference numerals in the drawings indicate the same or corresponding parts.

Claims (1)

[Claims] 1. A relational expression between a voltage v and a current i of a power system, which are sampled at even intervals by a multipoint sampling, and a resistance R and an inductance L of a transmission line From t ₀ , t ₁ … t _n-1 , t _n , t _{n + 1} ,…
t _2n 2 equations are obtained and the integral operation in the equations Against Where K ₁ , K ₂ … K _{n + 1} is a constant θ is the sampling angle i ₍₀₎ , i ₍₁₎ … i _(2n) is i at time t ₍₀₎ , t ₍₁₎ … t _(2n) A digital fault point locator characterized by finding R and L from these relational expressions by approximating by the instantaneous value of.